1994 AIME Problems/Problem 4
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Problem
Find the positive integer for which
(For real
,
is the greatest integer
)
Solution
Note that if for some
, then
.
Thus, there are integers
such that
. So the sum of
for all such
is
.
Let be the integer such that
. So for each integer
, there are
integers
such that
, and there are
such integers such that
.
Therefore, .
Through computation: and
. Thus,
.
So, .
See also
1994 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 3 |
Followed by Problem 5 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |